Question

Please help!! Which number is greater? a)The square root of 64 b) The square root of 16

Answer 1

Answer:

Neither, they are both equal.

Step-by-step explanation:

FYI, that three in front of the radical in the first expression is actually cube root. The cube root of 64 is 4, and the square root of 16 is 4.

$\sqrt[3]{64} =4\\\sqrt{16}=4\\4=4$

Answer 2

$\huge\text{Hey there!}$

$\huge\textsf{Option A }\huge\boxed {\downarrow}$

$\huge\boxed{\rm{\sqrt[3]{64}}}}\\\huge\boxed{= \rm{\sqrt[3]{4^3}}}}\\\huge\boxed{= \rm{\sqrt[3]{4\times4 \times4}}}\\\huge\boxed{\rm{\rightarrow \sqrt{64}= 8, \ because \ 8\times8 = \bf 64}}\\\huge\boxed{\rm{{= \dfrac{8}{2}\rightarrow 8\div 2 \rightarrow \bf 4}}}$

$\huge\boxed{\textsf{Option A.) answer: \bf 4}}$

$\huge\textsf{Possible Option A. part II }\huge\boxed\downarrow$

$\huge\boxed{\rm{\sqrt{64} = \sqrt{8\times8}= \bf 8}}\\\huge\boxed{\text{Possible answer for Option A. part II: \bf 8}}$

$\huge\textsf{Option B }\huge\boxed\downarrow$

$\huge\boxed{\rm{\sqrt{16}}}\\\huge\boxed{\rm{= \sqrt{4\times4}}}\\\huge\boxed{\rm{= \sqrt{16} \rightarrow \bold{4}\rightarrow 4\times4 \rightarrow \bf 16}}$

$\huge\boxed{\textsf{Option B.) answer: \bf 4}}$

$\huge\boxed{{\textsf{Based on the given information \boxed{\textsf{\bf NEITHER}} is}}}\\\huge\boxed{\textsf{the answer because it seems reasonable \& both}}\\\huge\boxed{\textsf{choices are very much equivalent to each other}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$